Problem: Simplify the following expression: $ n = \dfrac{-5}{3} - \dfrac{-3y + 4}{-6y - 2} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-6y - 2}{-6y - 2}$ $ \dfrac{-5}{3} \times \dfrac{-6y - 2}{-6y - 2} = \dfrac{30y + 10}{-18y - 6} $ Multiply the second expression by $\dfrac{3}{3}$ $ \dfrac{-3y + 4}{-6y - 2} \times \dfrac{3}{3} = \dfrac{-9y + 12}{-18y - 6} $ Therefore $ n = \dfrac{30y + 10}{-18y - 6} - \dfrac{-9y + 12}{-18y - 6} $ Now the expressions have the same denominator we can simply subtract the numerators: $n = \dfrac{30y + 10 - (-9y + 12) }{-18y - 6} $ Distribute the negative sign: $n = \dfrac{30y + 10 + 9y - 12}{-18y - 6}$ $n = \dfrac{39y - 2}{-18y - 6}$ Simplify the expression by dividing the numerator and denominator by -1: $n = \dfrac{-39y + 2}{18y + 6}$